In a previous publication, we have examined the fundamental difference
between computational precision and result accuracy in the context of
the iterative solution of linear systems as they typically arise in the
Finite Element discretization of Partial Differential Equations (PDEs).
In particular, we evaluated mixed- and emulated-precision schemes on
commodity graphics processors (GPUs), which at that time only supported
computations in single precision. With the advent of graphics cards that
natively provide double precision, this report updates our previous results.
We demonstrate that with new co-processor hardware supporting native
double precision, such as NVIDIA`s G200 and T10 architectures, the
situation does not change qualitatively for PDEs, and the previously
introduced mixed precision schemes are still preferable to double
precision alone. But the schemes achieve significant quantitative
performance improvements with the more powerful hardware. In particular,
we demonstrate that a Multigrid scheme can accurately solve a common
test problem in Finite Element settings with one million unknowns in
less than 0.1 seconds, which is truely outstanding performance. We
support these conclusions by exploring the algorithmic design space
enlarged by the availability of double precision directly in the hardware.
Note: also published on /url{http://www.gpucomputing.org}